Generalized negacyclic codes over finite fields
Linear codes with additional algebraic structures such as cyclic codes, negacyclic codes and abelian codes have become of interest due to their nice algebraic structures, wide applications and links with other mathematical objects. In this paper, a generalization of negacyclic codes is introduced...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/161225 |
| _version_ | 1826120910301560832 |
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| author | Jitman, Somphong Ling, San Tharnnukhroh, Jareena |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Jitman, Somphong Ling, San Tharnnukhroh, Jareena |
| author_sort | Jitman, Somphong |
| collection | NTU |
| description | Linear codes with additional algebraic structures such as cyclic codes, negacyclic
codes and abelian codes have become of interest due to their nice algebraic structures,
wide applications and links with other mathematical objects. In this paper, a
generalization of negacyclic codes is introduced and studied. Algebraic structures of
such codes are given though cyclotomic classes of abelian groups and ideals in twisted
group algebras. Recursive constructions and enumerations of such codes are presented.
Characterizations of self-dual generalized negacyclic codes and complementary dual
generalized negacyclic codes are given as well as their enumerations. |
| first_indexed | 2024-10-01T05:24:10Z |
| format | Journal Article |
| id | ntu-10356/161225 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T05:24:10Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-10356/1612252022-08-22T01:59:28Z Generalized negacyclic codes over finite fields Jitman, Somphong Ling, San Tharnnukhroh, Jareena School of Physical and Mathematical Sciences Science::Mathematics::Algebra Science::Mathematics::Applied mathematics::Information theory Cyclotomic Classes Negacyclic Codes Linear codes with additional algebraic structures such as cyclic codes, negacyclic codes and abelian codes have become of interest due to their nice algebraic structures, wide applications and links with other mathematical objects. In this paper, a generalization of negacyclic codes is introduced and studied. Algebraic structures of such codes are given though cyclotomic classes of abelian groups and ideals in twisted group algebras. Recursive constructions and enumerations of such codes are presented. Characterizations of self-dual generalized negacyclic codes and complementary dual generalized negacyclic codes are given as well as their enumerations. Nanyang Technological University The research of S. Ling is partially supported by Nanyang Technological University Research Grant No. 04INS000047C230GRT01. 2022-08-22T01:59:28Z 2022-08-22T01:59:28Z 2022 Journal Article Jitman, S., Ling, S. & Tharnnukhroh, J. (2022). Generalized negacyclic codes over finite fields. Journal of Applied Mathematics and Computing. https://dx.doi.org/10.1007/s12190-022-01753-8 1598-5865 https://hdl.handle.net/10356/161225 10.1007/s12190-022-01753-8 en 04INS000047C230GRT01 Journal of Applied Mathematics and Computing © 2022 The Author(s) under exclusive licence to Korean Society for Informatics and Computational Applied Mathematics. All rights reserved. |
| spellingShingle | Science::Mathematics::Algebra Science::Mathematics::Applied mathematics::Information theory Cyclotomic Classes Negacyclic Codes Jitman, Somphong Ling, San Tharnnukhroh, Jareena Generalized negacyclic codes over finite fields |
| title | Generalized negacyclic codes over finite fields |
| title_full | Generalized negacyclic codes over finite fields |
| title_fullStr | Generalized negacyclic codes over finite fields |
| title_full_unstemmed | Generalized negacyclic codes over finite fields |
| title_short | Generalized negacyclic codes over finite fields |
| title_sort | generalized negacyclic codes over finite fields |
| topic | Science::Mathematics::Algebra Science::Mathematics::Applied mathematics::Information theory Cyclotomic Classes Negacyclic Codes |
| url | https://hdl.handle.net/10356/161225 |
| work_keys_str_mv | AT jitmansomphong generalizednegacycliccodesoverfinitefields AT lingsan generalizednegacycliccodesoverfinitefields AT tharnnukhrohjareena generalizednegacycliccodesoverfinitefields |